Status and applicability of solid polymer electrolyte technology to electrolytic hydrogen and oxygen production

The solid polymer electrolyte (SPE) water electrolysis technology is presented as a potential energy conversion method for wind driven generator systems. Electrolysis life and performance data are presented from laboratory sized single cells (7.2 sq in active area) with high cell current density selected (1000 ASF) for normal operation

Hierarchical Gaussian process mixtures for regression

As a result of their good performance in practice and their desirable analytical properties, Gaussian process regression models are becoming increasingly of interest in statistics, engineering and other fields. However, two major problems arise when the model is applied to a large data-set with repeated measurements. One stems from the systematic heterogeneity among the different replications, and the other is the requirement to invert a covariance matrix which is involved in the implementation of the model. The dimension of this matrix equals the sample size of the training data-set. In this paper, a Gaussian process mixture model for regression is proposed for dealing with the above two problems, and a hybrid Markov chain Monte Carlo (MCMC) algorithm is used for its implementation. Application to a real data-set is reported

Learning Mixtures of Gaussians in High Dimensions

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the covariance matrices of these Gaussians. This learning problem arises in many areas ranging from the natural sciences to the social sciences, and has also found many machine learning applications. Unfortunately, learning mixture of Gaussians is an information theoretically hard problem: in order to learn the parameters up to a reasonable accuracy, the number of samples required is exponential in the number of Gaussian components in the worst case. In this work, we show that provided we are in high enough dimensions, the class of Gaussian mixtures is learnable in its most general form under a smoothed analysis framework, where the parameters are randomly perturbed from an adversarial starting point. In particular, given samples from a mixture of Gaussians with randomly perturbed parameters, when n > {\Omega}(k^2), we give an algorithm that learns the parameters with polynomial running time and using polynomial number of samples. The central algorithmic ideas consist of new ways to decompose the moment tensor of the Gaussian mixture by exploiting its structural properties. The symmetries of this tensor are derived from the combinatorial structure of higher order moments of Gaussian distributions (sometimes referred to as Isserlis' theorem or Wick's theorem). We also develop new tools for bounding smallest singular values of structured random matrices, which could be useful in other smoothed analysis settings

Microstructure Effects on Daily Return Volatility in Financial Markets

We simulate a series of daily returns from intraday price movements initiated by microstructure elements. Significant evidence is found that daily returns and daily return volatility exhibit first order autocorrelation, but trading volume and daily return volatility are not correlated, while intraday volatility is. We also consider GARCH effects in daily return series and show that estimates using daily returns are biased from the influence of the level of prices. Using daily price changes instead, we find evidence of a significant GARCH component. These results suggest that microstructure elements have a considerable influence on the return generating process.Comment: 15 pages, as presented at the Complexity Workshop in Aix-en-Provenc

D-optimal designs via a cocktail algorithm

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey, Titterington and Torsney, 1978), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either the multiplicative algorithm or the vertex exchange method (a variant of VDM). Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.Comment: A number of changes after accounting for the referees' comments including new examples in Section 4 and more detailed explanations throughou

Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset.Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical Society of Americ

On the kinematic deconvolution of the local neighbourhood luminosity function

A method for inverting the statistical star counts equation, including proper motions, is presented; in order to break the degeneracy in that equation it uses the supplementary constraints required by dynamical consistency. The inversion gives access to both the kinematics and the luminosity function of each population in three r\'egimes: the singular ellipsoid, the constant ratio Schwarzschild ellipsoid plane parallel models and the epicyclic model. This more realistic model is taylored to account for local neighbourhood density and velocity distribution. The first model is fully investigated both analytically and via means of a non-parametric inversion technique, while the second model is shown to be formally its equivalent. The effect of noise and incompleteness in apparent magnitude is investigated. The third model is investigated via a 5D+2D non-parametric inversion technique where positivity of the underlying luminosity function is explicitely accounted for. It is argued that its future application to data such as the Tycho catalogue (and in the upcoming satellite GAIA) could lead -- provided the vertical potential, and/or the asymmetric drift or w_0 are known -- to a non-parametric determination of the local neighbourhood luminosity function without any reference to stellar evolution tracks. It should also yield the proportion of stars for each kinematic component and a kinematic diagnostic to split the thin disk from the thick disk or the halo.Comment: 18 pages, LateX (or Latex, etc), mnras, accepted for publicatio

Characterizing and Improving Generalized Belief Propagation Algorithms on the 2D Edwards-Anderson Model

We study the performance of different message passing algorithms in the two dimensional Edwards Anderson model. We show that the standard Belief Propagation (BP) algorithm converges only at high temperature to a paramagnetic solution. Then, we test a Generalized Belief Propagation (GBP) algorithm, derived from a Cluster Variational Method (CVM) at the plaquette level. We compare its performance with BP and with other algorithms derived under the same approximation: Double Loop (DL) and a two-ways message passing algorithm (HAK). The plaquette-CVM approximation improves BP in at least three ways: the quality of the paramagnetic solution at high temperatures, a better estimate (lower) for the critical temperature, and the fact that the GBP message passing algorithm converges also to non paramagnetic solutions. The lack of convergence of the standard GBP message passing algorithm at low temperatures seems to be related to the implementation details and not to the appearance of long range order. In fact, we prove that a gauge invariance of the constrained CVM free energy can be exploited to derive a new message passing algorithm which converges at even lower temperatures. In all its region of convergence this new algorithm is faster than HAK and DL by some orders of magnitude.Comment: 19 pages, 13 figure

An approximate Bayesian marginal likelihood approach for estimating finite mixtures

Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior model, a computationally efficient stochastic approximation version of the marginal likelihood is proposed and large-sample theory is presented. By restricting the support to a finite grid, a simulated annealing method is employed to maximize the marginal likelihood and estimate the support. Real and simulated data examples show that this novel stochastic approximation--simulated annealing procedure compares favorably to existing methods.Comment: 16 pages, 1 figure, 3 table

Millihertz X-ray variability during the 2019 outburst of black hole candidate Swift~J1357.2−-0933

Swift J1357.2$-$0933 is a black-hole candidate X-ray transient, which underwent its third outburst in 2019, during which several multi-wavelength observations were carried out.~Here, we report results from the \emph{Neil Gehrels Swift} and \emph{NICER} observatories and radio data from \emph{AMI}.~For the first time,~millihertz quasi-periodic X-ray oscillations with frequencies varying between ${\sim}$~1--5~$\rm{mHz}$ were found in \emph{NICER} observations and a similar feature was also detected in one \emph{Swift}--\textsc{XRT} dataset.~Our spectral analysis indicate that the maximum value of the measured X-ray flux is much lower compared to the peak values observed during the 2011 and 2017 outbursts.~This value is ${\sim}$~100 times lower than found with \emph{MAXI} on MJD~58558 much ($\sim$~68 days) earlier in the outburst, suggesting that the \emph{Swift} and \emph{NICER} fluxes belong to the declining phase of the 2019 outburst.~An additional soft component was detected in the \textsc{XRT} observation with the highest flux level, but at a relatively low $L_{\rm X}$~$\sim$~$3{\times}10^{34}~(d/{\rm 6~kpc)}^2\rm{erg}~\rm{s}^{-1}$, and which we fitted with a disc component at a temperature of $\sim 0.17$~keV.~The optical/UV magnitudes obtained from \emph{Swift}--\textsc{UVOT} showed a correlation with X-ray observations, indicating X-ray reprocessing to be the plausible origin of the optical and UV emission.~However, the source was not significantly detected in the radio band.~There are currently a number of models that could explain this millihertz-frequency X-ray variability; not least of which involves an X-ray component to the curious dips that, so far, have only been observed in the optical.Comment: 14 pages, Accepted for publication in MNRA